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Day 87: CDS Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Polynomials. Asked once: CDS 2 2025 (same type asked 9 times) See all 9 of this type

    16
    What is the HCF of x3+y3+3xy−1x^3+y^3+3xy-1 and (x+y)4−1(x+y)^4-1?

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  2. Question 2

    Number System. Asked once: CDS 1 2025 (same type asked 8 times) See all 8 of this type

    48
    What is the number of factors of 243−163−8324^3 - 16^3 - 8^3 ?

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  3. Question 3

    Number System. Asked once: CDS 2 2025 (same type asked 8 times) See all 8 of this type

    83
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : The last digit in the expansion of the number (54D)100(54D)^{100} is 1. What is the value of the digit DD? Statement-I : D>5D > 5 Statement-II : DD is a multiple of 3. Which one of the following is correct in respect of the above Question and the Statements?

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  4. Question 4

    Mensuration 2D. Asked once: CDS 2 2022 (same type asked 8 times) See all 8 of this type

    95
    A triangle has side lengths x cm, x + 13 cm and x + 26 cm. If its area is 126 square cm, then what is the value of x ?

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  5. Question 5

    Trigonometric Ratios and Identities. Asked once: CDS 1 2023 (same type asked 8 times) See all 8 of this type

    47
    If sin⁡θ=1213\sin\theta = \frac{12}{13}, then what is the value of (tan⁡θ+sec⁡θ)2(cosec⁡ θ−cot⁡θ)−2(\tan\theta + \sec\theta)^2 (\operatorname{cosec}\,\theta - \cot\theta)^{-2}, 0<θ<π20 < \theta < \frac{\pi}{2} ?

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